The assessment of diagnostic markers for classification and prediction in two-class problems is commonly performed with the use of Receiver Operating Characteristic (ROC) curves. The ROC curve is a graphical representation of True Positive Rates (TPR; sensitivity) versus False Positive Rates (FPR; 1-specificity). It is defined by considering a classification criterion over all possible values for the two classes under study (commonly referred to as the diseased and healthy populations). The area under the ROC curve (AUC) can be used as a global measure of the ability of this classification criterion to distinguish between these two populations under consideration. Statistical inference is based on U-statistic (non-parametric) or parametric estimation of the AUC and its standard error. In three-class diagnostic problems, three True Class Rates (TCR) are defined as a direct generalization of the two-class case and can easily be extended in multiple-class classification problems. In the three-class situation, an ROC surface is generated in three dimensions by considering all possible values of the test. As a natural generalization of the area under the ROC curve, the volume under the ROC surface (VUS) can be used as a global measure of the ability of the test to discriminate between three groups. Estimates of the VUS and its standard error are generated using U-statistics or bootstrap methodology. These formulations can be used whenever the diagnostic marker measurements are continuous or ordered categories. A classification of three groups of subjects based on an imaging marker is described in an example.